Related papers: A Data-Driven Approach to Solving First-Kind Fredh…
Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based…
We present a novel space-time isogeometric discretization of the acoustic wave equation in second-order formulation that is intrinsically unconditionally stable. The method relies on a variational framework inspired by [Walkington 2014],…
This article presents near-optimal guarantees for accurate and robust image recovery from under-sampled noisy measurements using total variation minimization. In particular, we show that from O(slog(N)) nonadaptive linear measurements, an…
For systems of ordinary differential equations on a compact interval, we study the character of solvability of the most general linear boundary-value problems in Sobolev spaces. We find the indices of these problems and obtain a criterion…
This work theoretically studies the problem of estimating a structured high-dimensional signal $x_0 \in \mathbb{R}^n$ from noisy $1$-bit Gaussian measurements. Our recovery approach is based on a simple convex program which uses the hinge…
Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…
This paper is concerned with estimation of multiple frequencies from incomplete and/or noisy samples based on a low-CP-rank tensor data model where each CP vector is an array response vector of one frequency. Suppose that it is known a…
We solve first-kind Fredholm boundary integral equations arising from Helmholtz and Laplace problems on bounded, smooth screens in three-dimensions with either Dirichlet or Neumann conditions. The proposed Galerkin-Bubnov method takes as…
We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements of the solution on a surface outside the support of the…
We provide a new estimator of integral operators with smooth kernels, obtained from a set of scattered and noisy impulse responses. The proposed approach relies on the formalism of smoothing in reproducing kernel Hilbert spaces and on the…
We design a primal-dual stabilized finite element method for the numerical approximation of a data assimilation problem subject to the acoustic wave equation. For the forward problem, piecewise affine, continuous, finite element functions…
We consider the problem of positioning a cloud of points in the Euclidean space $\mathbb{R}^d$, using noisy measurements of a subset of pairwise distances. This task has applications in various areas, such as sensor network localization and…
In this paper we derive information theoretic performance bounds to sensing and reconstruction of sparse phenomena from noisy projections. We consider two settings: output noise models where the noise enters after the projection and input…
Frequency recovery/estimation from discrete samples of superimposed sinusoidal signals is a classic yet important problem in statistical signal processing. Its research has recently been advanced by atomic norm techniques which exploit…
We study the problem of optimizing a function under a \emph{budgeted number of evaluations}. We only assume that the function is \emph{locally} smooth around one of its global optima. The difficulty of optimization is measured in terms of…
In this paper we consider the problem of recovering the conformal factor in a conformal class of Riemannian metrics from the boundary measurement of one wave field. More precisely, using boundary control operators, we derive an explicit…
We study the Inexact Restoration framework with random models for minimizing functions whose evaluation is subject to errors. We propose a constrained formulation that includes well-known stochastic problems and an algorithm applicable when…
Signal recovery from incomplete or partial frequency information is a fundamental problem in harmonic analysis and applied mathematics, with wide-ranging applications in communications, imaging, and data science. Historically, the classical…
We present a new filtered low-regularity Fourier integrator for the cubic nonlinear Schr\"odinger equation based on recent time discretization and filtering techniques. For this new scheme, we perform a rigorous error analysis and establish…
We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking…